Calculus I = Math C075, Temple U., Fall 2002

Calculus I is the first half of a two-semester course. The next semester is Calculus II, math 76. The 7-series is usually taken by non-math majors such as biology and chemistry.

Warren D. Smith, Instructor

MSRC:

The Math Resource Center in basement of Curtis hall - free tutoring, has textbook library, books, computers, hard to beat that! And here is its web page.

Also: Emily Warner, Math ombudsperson (email: ewarner@math.temple.edu) is in 6th floor lounge Wachman MWF 1:30-3:30 to help you

Textbook:

Hughes-Hallett/Gleasom/etc: Calculus - single variable (3rd ed), John Wiley 2002.

(You do not need to buy the "solution guide", which is some additional lookalike book.)

This book will also be re-used in math 76 (the followup course next semester). It comes as looseleaf sheets, which you need to insert in a 3-ring binder (that is the way it is with my copy, anyway). Makes it cheaper. Note, this is really two books, one is the book per se, and has an index. At the beginning and end there are handy quick reference lists of useful formulas. On page 582 there is a handy condensed summary of the useful stuff in the book. Handy for reviewing before exams! The second book is "student study guide" containing questions, examples, practice tests, worked problems & solutions.

Other useful books

Probably the single most useful math book on the planet - and cheap too! - is the big fat:

M.Abramowitz & I.Stegun (eds.): HANDBOOK OF MATHEMATICAL FUNCTIONS, U.S.Govt printing office (hardcover), & Dover (softcover).

If you want to be any kind of engineer, scientist, or computer programmer, then you'll want to own this book, so may as well buy it now and gain the advantages.

Also good, and of the same ilk, is

D.Zwillinger (ed.): CRC STANDARD MATHEMATICAL TABLES AND FORMULAE, CRC Press (30th+ edition).

Those 2 handbooks are useful as references - they collect lots of useful formulae and facts - but much less useful for understanding how those formulae & facts got there.

I'm not sure what the best books on calculus (covered in math 75 & 76) and multidimensional calculus (partly covered in math 76) are. Quite possibly it is not the one we are using.

James Stewart: CALCULUS (Brooks-Cole) looks good.

One classic textbook used successfully by many schools, is

G.Thomas & R.Finney: CALCULUS. (Now in its 10th edition. Addison-Wesley. May have "and analytic geometry" added at end of title, and/or may be more than 1 volume, depending on edition.)

But it'll cost you, probably over $100. Another classic book (more appreciated by experts, but probably too hard for beginners - but it is a lot cheaper than the above!) is

E.Whittaker & G.Watson: MODERN ANALYSIS (Cambridge Univ. Press)

Here's some cheap books that got good reviews from Sufferin' Students: And here is a cheap, easy-to-read book that has a lot of insights about mathematical thinking, including "method of induction" (it is not about calculus, though): G.Polya: How to solve it, Princeton Univ. Press 1957.

What is calculus good for?

Calculus (the topic of math 75 & 76), ordinary (somewhat covered in Math 76) and partial differential equations, and Matrices (these last 2 are not covered in 75 & 76) are the language and the building blocks of science and engineering. They are used in everything. If you learn calculus well you'll be able to do well in lots of other courses that depend on it. If you learn calculus badly it'll hurt you in all those other courses. Newton's laws of Physics, which are the key behind all machines, cars, planes, medical devices, animals that walk, fly, or swim, engines, explosions, the weather, motorcycle jumping, falling objects, motion of planets, energy, etc. are differential equations. So without differential equations (and the notion of a derivative) you can't even talk about that stuff. And all the physics more advanced than Newton's laws (governing chemistry, electronics, waves, fluids) uses partial differential equations. The basic mathematical functions like sin(x), log(x), etc, which will be totally understood through calculus, are used everywhere too. Another thing you'll learn how to do with calculus is computing areas, volumes, surface areas, and curve lengths. It also gives you ways to make approximations. How can you compute pi, or sin(1.34), to 50 decimal places? You'll find out how. Finally, calculus is also good for optimizing things. Suppose you design something. You want the design to be the best. So you optimize it. Calculus tells you how to optimize.

A 1st year physics course should synergise well with Calculus - both would help with the other. If you are taking physics, and you know calculus, you'll eat for lunch all the physics students who don't.

What John von Neumann thought about calculus

Syllabus

4 hours of classes a week for 14 weeks = 56 hours total = 28 lectures total. Note these plans (44 total hours) leave 12 extra leftover hours for reviews, tests, screwups, extra content, etc.:

Math 75:    topic            estim. # lecture hours  cum. total
-----------------------------------------------------------------
ch 1. Library of functions                      8      8
      [polynomials rational power exponential log trig]
ch 2. the derivative & the "limit" concept      8     16
ch 3. techniques of differentiation            12     28
      [chain rule, sum, product, divide, inverse, various functions]
ch 4. using derivative                         10     38
      [maxima, minima, Newton's method, optimizing, power series]
ch 5. definite integral                         6     44
      [fundamental thm of calculus, Riemann sums, Numerical
      integration.]
-----------------------------------------------------
Final exam: Tues 17 Dec, 2:00-4:00 PM, room CH309.
Covers: ch. 1, 2, 3.1-3.7, 3.9, 3.10, 4.1-4.3, 4.5, 5.
1-page long (8.5x11 inch, both sides) "crib sheet" is permitted.

Grading

Homework:               33.3%  (includes both kinds)
Final:                  33.3
Quizzes:                33.3

There will be two kinds of homework.

  1. COW ("calculus on web" - click here to get to http://cow.math.temple.edu) is a Temple University system which poses you calculus problems. Then you solve them and type in the answer. It is sort of like a video game. Once you get used to it, it is sort of fun. Instant feedback. If you get the wrong answer, it gives you hints and you can try again until you get the right answer (no penalty for wrong answers!). Your grade is automatically computed and stored in a cyberspace little black book. Important things to know about COW:
  2. But, let's face it, the problems on COW are shallow, and it also, annoyingly, forces you to do some problems like a robot rather than a human ("do you want to use method 1 or method 2?"). And you need to do some deeper problems involving actually applying pen to paper and actually writing sentences explaining what you are doing. I will hand out problem sets on wednesdays and they will be due the following monday. On wednesdays we will go over the problems from last week. The problem sets may include lists of COW problem numbers (these not to be solved on paper, but on the COW system) as well as actual pen-and-ink problems.
You have to do both kinds of problems (COW and regular). My Policies. Do not cheat on exams. In my classes, on written homework only, you can get help from others, but all such help must be acknowledged in writing ("Joe Blow helped me with problem 7"). This may result in less credit, e.g. if you just copied like a monkey. The object is for you to learn, and I realize in some cases you can learn better by getting help. (Warning: some professors do not feel that way - assume they do not permit help on homework unless they say they do!) In no case can you learn better by being a monkey. If you work out the problems yourself you'll definitely learn and get better, and then you'll be able to get a better grade on other stuff. Trying to cheat on COW is just stupid, since you never lose anything for wrong answers and can just keep trying until you get it right. If you feel you are in such trouble you have to do something like that, it'd probably be better for you to admit you are in trouble and arrange to take a less advanced class instead.

Prerequisites / Background knowledge (click here)

Useful links (click on them with your mouse)

Useful notes I wrote to help you ;)

In-class quizzes

About the department-wide final exam

The question sets from several previous math75 final exams are now available online! [Note. Unlike the exams in (or some of the exams in) my class, these finals contain many "multiple choice" questions. I do not know if any partial credit was awarded in cases of wrong finals answers - and suspect not, especially for the multiple choice ones. These finals all are closed-book and no-notes exams. Also note: these previous exams were based on a course with a differenttextbook so the curriculum has somewhat changed now.]

Final exam: Tues 17 Dec, 2:00-4:00 PM, room CH309. 1-page long (8.5x11 inch, both sides) "crib sheet" is permitted. Review session: Somebody named "Whondel" is doing one for math75 10am-12 Dec 12 in TL103. If you can't make it, then go to the math76 review session (also by Whondel) in CH11/13 at 12:30-2:30pm. Also feel free to send me email and/or try to visit me in my office for help.

Extra credit problems - a fine opportunity!

Homework

I expect a comparable amount of time may be spent each week on homework as is spent in class! I.e. your homework problems are going to be pretty hard. They may require looking up stuff in books, and may require developing multistep plans to solve the problem, and executing the plans, and doing sanity checks to help make sure your plans and execution worked! YES, I'd like to have the homework cover only (or almost only) material we have already covered in class (although you may have to invent new ways to combine those ideas), but I admit that I was not too good at achieving that goal at the beginning.